Peters Jörg
IEEE Comput Graph Appl. 2012 May-Jun;32(3):88-93. doi: 10.1109/MCG.2012.51.
In computer graphics and geometric modeling, changing the variables is a useful technique that appears in many guises. It lets us change how we traverse curves or surfaces, modify their derivatives or place, and interpret textures or other properties associated with them. It is shown that while changing variables of a parametric curve or surface leaves its geometric shape untouched, changing the way we associate parameters to curves or surfaces does have an impact: computer graphics deals with sampled geometry, and the sampled geometry changes. We can take advantage of the change of variables to improve how the surface is textured. Moreover, change of variables makes it possible to combine curve segments or curved surface patches into a smooth ensemble when the shape is more general than the graph of a function.
在计算机图形学和几何建模中，变量变换是一种以多种形式出现的有用技术。它使我们能够改变遍历曲线或曲面的方式、修改其导数或位置，并解释与其相关的纹理或其他属性。结果表明，虽然参数曲线或曲面的变量变换不会改变其几何形状，但改变我们将参数与曲线或曲面关联的方式确实会产生影响：计算机图形学处理的是采样几何，而采样几何会发生变化。我们可以利用变量变换来改进曲面的纹理映射方式。此外，当形状比函数图像更一般时，变量变换使得将曲线段或曲面片组合成一个平滑的整体成为可能。
